We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

From the Publisher: 
The accessible presentation of this book gives both a general view of the entire computer vision enterprise and also offers sufficient detail to be able to build useful applications. Users learn techniques that have proven to be useful by first-hand experience and a wide range of mathematical methods. A CD-ROM with every copy of the text contains source code for programming practice, color images, and illustrative movies. Comprehensive and up-to-date, this book includes essential topics that either reflect practical significance or are of theoretical importance. Topics are discussed in substantial and increasing depth. Application surveys describe numerous important application areas such as image based rendering and digital libraries. Many important algorithms broken down and illustrated in pseudo code. Appropriate for use by engineers as a comprehensive reference to the computer vision enterprise.

Computer vision : a modern approach = 计算机视觉 : 一种现代的方法

The notion of dynamic capabilities complements the premise of the resource-based view of the firm, and has injected new vigour into empirical research in the last decade Nonetheless, several issues surrounding its conceptualization remain ambivalent In light of empirical advancement, this paper aims to clarify the concept of dynamic capabilities, and then identify three component factors which reflect the common features of dynamic capabilities across firms and which may be adopted and further developed into a measurement construct in future research Further, a research model is developed encompassing antecedents and consequences of dynamic capabilities in an integrated framework Suggestions for future research and managerial implications are also discussed

https://repository.royalholloway.ac.uk/items/591eb589-5df7-45b1-89e0-6ed34222d85d/1/Wang%20C%20IJMR%20final.pdf

Dynamic capabilities: A review and research agenda

The literature on case studies, both in the field of international business (IB) and in the social sciences more generally, has tended to focus on the methods of data production and analysis suited to this research strategy. In contrast, in this paper we investigate methods of theorising from case studies. We seek to understand how case researchers theorise, and how future IB research might utilise case studies for theorising. By means of a qualitative content analysis of case studies published in Journal of International Business Studies, Academy of Management Journal and Journal of Management Studies, we construct a typology of theorising from case studies. Two dimensions of the case study, namely causal explanation and contextualisation, form the basis for our typology. We distinguish four methods of theorising – inductive theory-building, interpretive sensemaking, natural experiment and contextualised explanation – only the first of which has been widely used in JIBS in the period that we investigate. On the basis of our own qualitative analysis, we show the limitations of inductive theory-building, and argue that greater utilisation of the other methods of theorising would enhance the case study's explanatory power and potential for contextualisation. We argue for a more pluralist future for IB research.

https://link.springer.com/content/pdf/10.1057%2Fjibs.2010.55.pdf

Theorising from Case Studies: Towards a Pluralist Future for International Business Research

Modern Graph Theory

We propose a distributed algorithm, named Distributed Alternating Direction Method of Multipliers (D-ADMM), for solving separable optimization problems in networks of interconnected nodes or agents. In a separable optimization problem there is a private cost function and a private constraint set at each node. The goal is to minimize the sum of all the cost functions, constraining the solution to be in the intersection of all the constraint sets. D-ADMM is proven to converge when the network is bipartite or when all the functions are strongly convex, although in practice, convergence is observed even when these conditions are not met. We use D-ADMM to solve the following problems from signal processing and control: average consensus, compressed sensing, and support vector machines. Our simulations show that D-ADMM requires less communications than state-of-the-art algorithms to achieve a given accuracy level. Algorithms with low communication requirements are important, for example, in sensor networks, where sensors are typically battery-operated and communicating is the most energy consuming operation.

D-ADMM: A Communication-Efficient Distributed Algorithm for Separable Optimization

We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP) BP finds the least l1-norm solution of the underdetermined linear system Ax = b and is used, for example, in compressed sensing for reconstruction Our algorithm solves BP on a distributed platform such as a sensor network, and is designed to minimize the communication between nodes The algorithm only requires the network to be connected, has no notion of a central processing node, and no node has access to the entire matrix A at any time We consider two scenarios in which either the columns or the rows of A are distributed among the compute nodes Our algorithm, named D-ADMM, is a decentralized implementation of the alternating direction method of multi- pliers We show through numerical simulation that our algorithm requires considerably less communications between the nodes than the state-of-the-art algorithms

/pdf/distributed-basis-pursuit-a1nbplmwju.pdf

Distributed Basis Pursuit

We address the problem of compressed sensing (CS) with prior information: reconstruct a target CS signal with the aid of a similar signal that is known beforehand, our prior information . We integrate the additional knowledge of the similar signal into CS via $\ell _{1}$ - $\ell _{1}$ and $\ell _{1}$ - $\ell _{2}$ minimization. We then establish bounds on the number of measurements required by these problems to successfully reconstruct the original signal. Our bounds and geometrical interpretations reveal that if the prior information has good enough quality, $\ell _{1}$ - $\ell _{1}$ minimization improves the performance of CS dramatically. In contrast, $\ell _{1}$ - $\ell _{2}$ minimization has a performance very similar to classical CS, and brings no significant benefits. In addition, we use the insight provided by our bounds to design practical schemes to improve prior information. All our findings are illustrated with experimental results.

/pdf/compressed-sensing-with-prior-information-strategies-18vp0zcug7.pdf

Compressed Sensing With Prior Information: Strategies, Geometry, and Bounds

We consider a network where each node has exclusive access to a local cost function. Our contribution is a communication-efficient distributed algorithm that finds a vector $x^{\star} $ minimizing the sum of all the functions. We make the additional assumption that the functions have intersecting local domains, i.e., each function depends only on some components of the variable. Consequently, each node is interested in knowing only some components of $x^{\star} $ , not the entire vector. This allows improving communication-efficiency. We apply our algorithm to distributed model predictive control (D-MPC) and to network flow problems and show, through experiments on large networks, that the proposed algorithm requires less communications to converge than prior state-of-the-art algorithms.

/pdf/distributed-optimization-with-local-domains-applications-in-27b69sil31.pdf

Distributed Optimization With Local Domains: Applications in MPC and Network Flows

Many problems in control can be modeled as an optimization problem over a network of nodes. Solving them with distributed algorithms provides advantages over centralized solutions, such as privacy and the ability to process data locally. In this paper, we solve optimization problems in networks where each node requires only partial knowledge of the problem's solution. We explore this feature to design a decentralized algorithm that allows a significant reduction in the total number of communications. Our algorithm is based on the Alternating Direction of Multipliers (ADMM), and we apply it to distributed Model Predictive Control (MPC) and TCP/IP congestion control. Simulation results show that the proposed algorithm requires less communications than previous work for the same solution accuracy.

/pdf/distributed-admm-for-model-predictive-control-and-congestion-4heajppi88.pdf

Joao F. C. Mota

Papers

D-ADMM: A Communication-Efficient Distributed Algorithm for Separable Optimization

Distributed Basis Pursuit

Compressed Sensing With Prior Information: Strategies, Geometry, and Bounds

Distributed Optimization With Local Domains: Applications in MPC and Network Flows

Distributed ADMM for model predictive control and congestion control